The best picks globally to counter Aatrox include Kalista, Aphelios, and Samira. These champs are all good at countering Aatrox with high win rates over 54%. Even if these Aatrox counter picks are not taken in your lane, it's not a good idea to play him into one of these matchups. They will usually destroy Aatrox.
Conversely, if the enemy team picks either Shaco or Taliyah, Aatrox mains should strongly think about selecting him, as he easily crushes these selections with win rates over 53% against both ofthem.